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Completeness is productive
Two procedures in bitopology
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A-morphism Banach spaces belongs Berlin bireflective C-morphism called Categorical Topology characterization closed sets coequalizer cofilament commutative compact Hausdorff compact spaces contains continuous functions continuous maps convergence spaces convex coreflective coreflective subcategory Corollary cotriple countable coZHD defined Definition denote diagram discrete disjoint duality E-closed embedding epimorphisms exists extension factorization filter finite following are equivalent forgetful functor full subcategory Hausdorff spaces Hence Herrlich homeomorphic homotopy implies induced initial completions injective isomorphism Kan extension Lecture Notes left adjoint Lemma lifting limit space locally compact monomorphism morphism N-space natural transformation nearness spaces object open sets pair Preprint preserves Proof Proposition prove quotient reflective reflexive resp respect right adjoint Saks space satisfies semi-topological functors semifinal sequence Springer Strecker structure functor subbase subset subspace supercompact Theorem theory Tholen topological categories topological functors topological spaces topologically algebraic topos uniform spaces unique University Wischnewsky